Getting started with animation accelartion?
Perhaps this will help you get the acceleration you want:

Blender Basic Animation - Using the Graph Editor and Interpolation Modes

https://www.youtube.com/watch?v=R9gCHhJOjlQ

In this intro, inascott888 positions a cube and keyframes location at the start frame, he then goes to the end frame, repositions the cube and keyframes location there. In the graph editor window, he then uses the bezier handles to change the shape of the transition curve, and shows how this can be used to effect acceleration of the cube (when the animation is played back), that is by making a very slow start, but increasingly steep curve up.